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Measures of Association and Impact

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  1. Measures of Associationand Impact Michael O’Reilly, MD, MPH FETP Thailand Introductory Course

  2. Objectives • Describe and calculate measures of association such as risk ratio and odds ratio, and describe when use each • Describe and calculate measures of public health impact such as attributable risk percent and population attributable risk percent

  3. Example for calculations: NHANES follow-up study Original enrollment 1971 – 1975 Follow-up 1982 – 1984 • Complete follow-up on: - 189 diabetic men - 3151 nondiabetic men - 218 diabetic women - 3823 nondiabetic women Participants aged 40-77 years at enrollment Ref: Kleinman J, et al. Mortality among diabetics in a national sample. AJE 1988; 128:389-401

  4. Risk # new cases during a specified periodsize of population at start of period = "Attack rate"= Probability of getting disease= Risk of disease= Cumulative incidence= Incidence proportion

  5. Example of Risk Calculation • Deaths in diabetic men 100 deaths189 men at start of follow-up period 2. Deaths in nondiabetic men 811 deaths3151 men at start of follow-up period

  6. Example of Risk Calculation • Deaths in diabetic men 100 deaths189 men at start of follow-up period Risk = 100/189 = 52.9%

  7. Example of Risk Calculation 2. Deaths in nondiabetic men 811 deaths3151 men at start of follow-up period Risk = 811/3151 = 25.7%

  8. Person-Time Rate # new cases during follow-up period # person-years of follow-up new cases during follow-up periodsum of the lengths of time each member of the population was at risk of disease = instantaneous incidence rate= Incidence density= "Person-time rate"

  9. Denominator of P-T Rate In a cohort (follow-up) study, follow each person until: • Onset of disease • Death • Loss to follow-up • End of study Add up the time each person was followed

  10. P-T Rate – Example Deaths in diabetic men If all enrolled in 1971, and if no deaths, and if all had been followed through 1984, denominator is: 189 × 13 = 2457 Person Years But some were enrolled 1972 - 1975, 100 died, & some were followed to 1982 or 1983. True denominator is: 1414.7 Person Years Rate = 100 / 1414.7 PY = 70.7 deaths / 1,000 PY (False rate 40.7 deaths/ 1,000 PY)

  11. Odds Odds in favor of an event = probability that event will occur probability that event will NOT occur Odds of disease = probability of disease 1 - probability of disease or, more simply, disease odds = # ill / # well

  12. Example of an Odds Calculation Deaths in diabetic men 100 deaths 189 men at start of follow-up period Probability of death = 100/189 = 52.9% Odds = probability of dying / probability of not dying = 0.529 / (1 - 0.529) = 0.529 / 0.471 = 1.1:1 Odds = # deaths / # survivors = 100 / 89 = 1.1:1

  13. Example of an Odds Calculation Odds of diabetes among men who died 100 deaths among diabetics 811 deaths among non-diabetics Prob. of diabetes = 100 / 911 = 0.110 = 11.0% ODDS = prob. of diabetes / prob. of non-diabetes = 0.110 / (1 - 0.110) = 0.110 / 0.890 = 1.23:1

  14. "Every epidemiologic studycan be summarized in a 2-by-2 table." - H. Ory

  15. Two-by-Two Tables Ill Well Total Risk Exposed a b H1 a/H1 Not exp c d H2 c/H2 Total V1 V2 T or N

  16. Mortality Among White Men, by Diabetic Status,NHANES Follow-up Study, 1982-1984 Dead Alive Total Risk Diabetic 100 89 189 52.9% Not 811 2340 315125.7% diabetic Total 91124293340 27.3%

  17. Measures of Association Quantify the relationship between an"exposure" and outcome of interest Quantify the difference in occurrence of disease or death between two groups of people who differ on "exposure“ Types of measures:−Ratios: relative risk, rate ratio, odds ratio−Difference: attributable risk

  18. Risk Ratio / Relative Risk Risk in "exposed" groupRisk in "unexposed" group EXAMPLE:Relative risk of death among diabetic men vs. nondiabetic men RR: ?

  19. Mortality Among White Men, by Diabetic Status,NHANES Follow-up Study, 1982-1984 Dead Alive Total Risk Diabetic 100 89 189 52.9% Not 811 2340 315125.7% diabetic Total 91124293340 27.3%

  20. Risk Ratio / Relative Risk Risk in "exposed" groupRisk in "unexposed" group EXAMPLE:Relative risk of death among diabetic men vs. nondiabetic men RR: 100/189.257 811/3151 .529 = 2.1

  21. Risk Ratio / Relative Risk Risk in "exposed" groupRisk in "unexposed" group EXAMPLE:Relative risk of illness for those who ate food A vs. those who did not eat food A RR: ?

  22. Risk Ratio / Relative Risk EXAMPLE:Relative risk of illness for those who ate food A vs. those who did not eat food A RR: .80 .14 = 5.7

  23. Questions about Risk Ratio Risk in "exposed" group Risk in "unexposed" group • What does RR > 1 mean?• What does RR = 1 mean?• What does RR < 1 mean?

  24. Comments about Risk Ratio • The further away from 1, the stronger the association between exposure and disease • Can only calculate Risk Ratio from cohort study

  25. Rate Ratio for P-T Rates Person-time rate in "exposed" groupPT rate in "unexposed" group Example:Death rate ratio among diabetic men vs. nondiabetic men RR =100/1414.7 =70.7/1000 = 2.5 811/28,029.8 =28.9/1000

  26. Comments about Rate Ratio The further away from 1, the stronger the association between exposure and disease Can only calculate Rate Ratio from follow-up cohort study

  27. Odds Ratio: General If you are not using cohort study data, then relative risk is not obtainable Under certain circumstances, odds ratios are good estimates of the relative risk

  28. Odds Ratio FORMULA 1 (“Disease Odds Ratio”): Odds of disease/death in “exposed” groupOdds of dz/death in “unexposed” group FORMULA 2 (“Exposure Odds Ratio”): Odds of being "exposed" among casesOdds of "exposed" among non-cases

  29. Disease Odds Ratio Dead Alive Odds of disease Diabetic 100 89 100/89 Not 811 2340 811/2340 Total 9112429 Using formula 1: OR 100/89 = 100 x 2340 = 3.2 811/2340 89 x 811

  30. Exposure Odds Ratio Dead Alive Diabetic 100 89 Not 811 2340 Odds of 100/81189/2340 Exposure Using formula 2: OR 100/811 = 100 x 2340 = 3.2 89/2340 89 x 811

  31. When Can the Odds Ratio be used to approximate the Relative Risk? Ill Well Total Risk Exposed a b a + ba/a + b Not exp c d c + dc/c + d RR = a/a+b ≈ a/b ≈ ad c/c+d c/d bc For a rare disease, a <<< b, so a+b ≈ b c <<< d, so c+d ≈ d

  32. Example of the “Rare Disease” Assumption? Ill Well Total Risk Exposed a b a + ba/a + b Not exp c d c + dc/c + d RR = a/a+b ≈ a/b ≈ ad c/c+d c/d bc For a rare disease, a <<< b, so a+b ≈ b c <<< d, so c+d ≈ d